| Table for sines of multiple angles (Notation: s = 2 sin x, t = 2 cos x) |
|---|
| 2 sin 2x = st |
| 2 sin 3x = s(t + 1)(t - 1) |
| 2 sin 4x = st(t2 - 2) |
| 2 sin 5x = s(t2 + t - 1)(t2 - t - 1) |
| 2 sin 6x = st(t + 1)(t - 1)(t2 - 3) |
| 2 sin 7x = s(t3 + t2 - 2t - 1)(t3 - t2 - 2t + 1) |
| 2 sin 8x = st(t2 - 2)(t4 - 4t2 + 2) |
| 2 sin 9x = s(t + 1)(t - 1)(t3 - 3t + 1)(t3 - 3t - 1) |
| 2 sin 10x = st(t2 + t - 1)(t2 - t - 1)(t4 - 5t2 + 5) |
| 2 sin 11x = s(t5 + t4 - 4t3 - 3t2 + 3t + 1)(t5 - t4 - 4t3 + 3t2 + 3t - 1) |
| 2 sin 12x = st(t + 1)(t - 1)(t2 - 2)(t2 - 3)(t4 - 4t2 + 1) |
| 2 sin 13x = s(t6 + t5 - 5t4 - 4t3 + 6t2 + 3t - 1)(t6 - t5 - 5t4 + 4t3 + 6t2 - 3t - 1) |
| 2 sin 14x = st(t3 + t2 - 2t - 1)(t3 - t2 - 2t + 1)(t6 - 7t4 + 14t2 - 7) |
| 2 sin 15x = s (t + 1)(t - 1)(t2 + t - 1)(t2 - t - 1)(t4 + t3 - 4t2 - 4t + 1)(t4 - t3 - 4t2 + 4t + 1) |
| 2 sin 16x = st(t2 - 2)(t4 - 4t2 + 2)(t8 - 8t6 + 20t4 - 16t2 + 2) |